Considerable effort has been devoted to development of computer codes because of the importance of numerical simulation in the study of impact cratering process (for example, the CTH code, McGlaun et al., 1990). In this research, we used iSALE2D (Wünnemann et al., 2006), which was developed on the basis of the SALE hydrocode (Amsden et al., 1980). The code was improved to include an elasto-plastic constitutive model, fragmentation models, various EoSs, and multiple materials (Ivanov et al., 1997; Melosh et al., 1992). A modified strength model (Collins et al., 2004) and a porosity compaction model (Wünnemann et al., 2006) have recently been included. All mechanic models, Newton’s laws of motion, and EoS constitute the physical principles behind the computer code (Melosh, 2007). Therefore, we will provide a thorough description of these models and list the corresponding parameters for Xiuyan crater simulation.
The rock types in a wide area surrounding the crater are composed of Proterozoic metamorphic rocks, including granulite, hornblendite, gneiss, tremolite marble, and marble (Chen et al., 2011), which shows that the target area is inhomogeneous in composition. Although including all of the above rock types into the hydrocode simulation is preferable, accomplishing such a task is virtually impossible, mostly because of the absence of the EoS for these rocks, especially under extremely high pressure and temperature. A general treatment in crater simulation involves simplifying the stratum with the primary component (e.g., Littlefield et al., 2007; Pierazzo and Melosh, 2000). Considering that the target material of Xiuyan crater pre-impact is mostly composed of Proterozoic crystalline, the target material is then simplified as granite in the hydrocode simulation, and such simplification is also used for the simulation of other terrestrial craters. For example, Ivanov and Artemieva (2011) also used granite to represent the target material of Popigai crater, in which layers of Archean gneisses covered with an inhomogeneous sedimentary and metasedimentary rock system existed.
For isolated small craters with diameters less than 2.5 km in the earth surface, most of the projectiles are composed of iron (Osinski and Pierazzo, 2013). This composition is because the iron meteoroid projectile is strong enough to withstand crushing from the atmosphere, while the stony projectile could be possibly destroyed, and a resulting crater field would be formed on the earth surface (Melosh, 1989). Although PGE anomaly and the existence of platina have been observed around Xiuyan crater (Qin et al., 2001), the primary composition of the projectile remains incompletely defined at present, and the projectile is also considered as an iron meteorite in the research.
The above treatments applied to target and projectile materials seem arbitrary. However, concerns regarding the set-up are unfounded, because upon the hypervelocity impact, the strength of these materials has been obscured by the extremely high shock pressure, although the strength may become important when the strength of the shock wave weakens. This research is aimed to interprete the formation and distribution of impact melt distribution, which is closely related with the pattern of shock pressure in the impact. Thus, the composition of materials should not exert a major effect on our conclusion, because the patterns of shock pressure are similar for different materials, as proven by physical experiments (Kinslow, 1970). Therefore, the derived distribution of impact melt should not be considerably affected by our selection of materials in this research.
Several categories of EoS currently describe the state of materials under shock pressure (Melosh, 1989). In this research, we used a kind of analytical EoS (ANEOS) to calculate the thermodynamic state of granite and iron (Thompson and Lauson, 1972), because the EoS includes a series of analytical expressions to describe the thermodynamic state surface (Littlefield, 1997; Melosh, 1989). The ANEOS was coded in FORTRAN programming language, and extensive input parameters must be provided to obtain the results (Thompson and Lauson, 1972). The iron ANEOS parameters are included in the code, whereas the parameters of granite can be referenced to Pierazzo et al. (1997).
The mechanical models in the hydrocode are used to describe material mechanical response to external deviator stress. These models are also extremely important in numerical modeling, because these models predict material deformation under the external force. In addition, the results of the laboratory experiments cannot be simply extrapolated to the scale of a natural impact, which also renders the mechanical models critical to the success of the simulation. In general, the more comprehensive the models means that more accurate results will be derived. In this research, we used the IVANOV of damage model, ROCK of the strength model, and the OHNAKA of the thermal softening model to simulate the mechanical properties of the materials. Yue et al. (2012) provided a short description of the above models, and the corresponding parameters with their descriptions are listed in Table 1.
Models Parameters Description Target Projectile IVANOV of damage model (Collins et al., 2004) ϵfb Minimum failure strain for low pressure states 10-4 10-4 B (Pa-1) Positive constant 10-11 10-11 pc (MPa) Pressure above which failure is always compressional 300.0 300.0 ROCK of strength model (Wünnemann et al., 2008) Yd0 (KPa) Cohesion of damaged material at zero pressure 10.0 0.01 μd Coefficient of internal friction for damaged material 0.6 0.4 Ydm (GPa) Limiting strength at high pressure for damaged material 2.5 1.7 Yi0 (MPa) Cohesion of intact material 10.0 5.0 μi Coefficient of internal friction for intact material 2.0 1.0 Yim (GPa) Limiting strength at high pressure for intact material 2.5 1.7 OHNAKA of thermal softening model (Ohnaka, 1995; Wünnemann et al., 2008) Tm0 (K) Melt temperature at zero pressure 1 673.0 1 811.0 a (GPa) Constant in Simon approximation 6.0 6.0 c Exponent in Simon approximation 3.0 3.0 ξ Constant in thermal softening law 1.2 1.2
Table 1. Parameters for mechanical models used in the research
Parameters Values Horizontal number cells from the left 0 : 150 : 200 Vertical number cells from the bottom 250 : 200 : 50 Extended factor 1.05 Grid spacing in high resolution 10 m Maximum grid spacing factor 20 Tracer numbers from target surface 100 : 150
Table 2. Parameters for the mesh used in the research
In the research, we first used scaling laws to estimate projectile diameters and duration time (Collins et al., 2005), and multiple models were then tested. In the best-fit model, the diameter of the projectile was 100 m, and the impact velocity was 17.0 km/s, which was the average impact velocity. Moreover, this velocity is sufficient to produce impact melt and vapor (O’Keefe and Ahrens, 1994).
In the simulation, we adopted cylindrical symmetry method to describe the target area. The impact point is located atthe center of the cylinder surface, and the projector center is situated on the vertical axis. The target material is under the projectile, and extends both horizontally and vertically to a distance far enough to reduce the effect of the reflected shock wave. To obtain a precise result while reducing the amount of calculation, only the center of the cylinder is set with a high resolution of 10 m, whereas the other regions are exaggerated at a factor of 1.05 times their previous cells, and a maximum exaggeration factor of 20 is set to the high resolution. The crater is completely represented in high resolution.
We set the tracers from the target surface down deep in high resolution, in which the state of the meshes can be tracked at each time step, and we can quantitatively analyze the impact melt material formation and evolvement with crater formation. Mesh parameters are listed in the following table.